Dynamic semantic accounts of presupposition have proven to quite successful improvements over earlier theories. One great advance has been to link presupposition and anaphora together (van der Sandt 92, Geurts 95), an approach that extends to integrate bridging and other discourse phenomena (Asher and Lascarides 1998a,b). In this extended anaphoric account, presuppositions attach, like assertions, to the discourse context via certain rhetorical relations. These discourse attachments constrain accommodation and help avoid some infelicitous predictions of standard accounts of presupposition. Further, they have interesting and complex interactions with underspecified conditions that are an important feature of the contributions of most presupposition triggers.
Deictic uses of definites, on the other hand, seem at first glance to fall outside the purview of an anaphoric theory of presupposition. There seems to be little that a discourse based theory would have to say. I will argue, however, that a discourse based account can capture how these definites function in conversation. In particular such accounts can clarify the interaction between the uses of such deictic definites and various conversational moves. At least some deictic uses of definites generate presuppositions that are bound to the context via a rhetorical function that I'll call unchoring, which if successful entails a type of knowing how. If this anchoring function is accepted, then the acceptors know how to locate the referent of the definite in the present context. I'll concentrate here just on definites that refer to spatial locations, where the intuitions about anchoring are quite clear. But I think that this view extends to other deictic uses of definites and has ramifications for an analysis of de re attitudes as well.